sure: Computes the minimum of the SURE thresholding function

In wavethresh: Wavelets Statistics and Transforms

Computes the minimum of the SURE thresholding function

Description

Computes the minimum of the SURE thresholding function for wavelet shrinkage as described in Donoho, D.L. and Johnstone, I.M. (1995) Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Ass., 90, 1200-1224.

Usage

sure(x)

Arguments

x	Vector of (normalized) wavelet coefficients. Coefficients should be supplied divided by their standard deviation, or some robust measure of scale

Details

SURE is a method for unbiasedly estimating the risk of an estimator. Stein (1981) showed that for a nearly arbitrary, nonlinear biased estimator, one can estimate its loss unbiasedly. See the Donoho and Johnstone, 1995 for further references and explanation. This function minimizes formula (11) from that paper.

Value

The absolute value of the wavelet coefficient that minimizes the SURE criteria

Author(s)

G P Nason

See Also

threshold

Examples

#
# Let's create "pretend" vector of wavelet coefficients contaminated with
# "noise".
#
v <- c(0.1, -0.2, 0.3, -0.4, 0.5, 99, 12, 6)
#
# Now, what's sure of this?
#
sure(v)
#
# [1] 0.5
#
#
# I.e. the large significant coefficients are 99, 12, 6 and the noise is
# anything less than this in abs value. So sure(v) is a good point to threshold
# at.

wavethresh documentation built on Sept. 11, 2024, 9:33 p.m.